Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2, 1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four- and five-dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to Abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2, 1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers-Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers-Perry solution. © 2007 IOP Publishing Ltd.
CITATION STYLE
Kunduri, H. K., Lucietti, J., & Reall, H. S. (2007). Near-horizon symmetries of extremal black holes. Classical and Quantum Gravity, 24(16), 4169–4189. https://doi.org/10.1088/0264-9381/24/16/012
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